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Home , 2020 NFL season, Bills Toronto Series, Buffalo (NFL), Giants Stadium, Lumen Field

Proceedings of International Mathematical Sciences ISSN:2717-6355, URL: https://dergipark.org.tr/tr/pub/pims Volume III Issue 1 (2021), Pages 10-24. DOI: https://doi.org/10.47086/pims.952438

COLD WEATHER TEAMS IN THE AND -FIELD ADVANTAGE

BRANDON JOLY* AND MEHMET DIK** *BELOIT, WISCONSIN, USA. **BELOIT, WISCONSIN, USA.

Abstract. The National Football League (NFL) has long had this idea of home-field advantage when teams play at home where they win more oftheir games. However, home games entail many things such as home fan atten- dance and weather. In considering the mean winning percentage of home games played during the winter months of December, January, and February by Cold Weather Teams, and the mean winning percentage of all home games played and all December, January, and February home games played, the null hypothesis would be that there is no difference in the means. By rejecting the null hypothesis, it would lead to the conclusion that cold weather plays a fac- tor in determining NFL games. This hypothesis testing is important because if teams in “colder weather climates” gain a significant advantage during the colder months of December, January, and February, the impacts of playing in an open grass during these months will have a greater impact on the and draft, which is decided based on final NFL standings. Thefinding is that Cold Weather Teams have a significant advantage when compared to the other data found, which suggests that cold weather tends to impact NFL games more than expected.

1. Introduction Before the start of the 2021 league year and since the 2002 , the NFL has been composed of 32 teams, each team playing 16 games, 8 of which are considered home games [1]. From 2002-2019, the NFL would play a total of 266 games that included a home team, which included playoff games, but excluded the which is played on a neutral field; however, in 2020, the NFL expanded the playoff field by one team in the Conference (AFC) and National Football Conference (NFC) to create 268 games that included a home team [2]. However, the 2020 NFL season is full of oddities, including changes to the schedule of 11 teams due to the Covid-19 pandemic [3], resulting in the Broncos without a starting (QB) play a game [4], and it is also the first time the host

2020 Mathematics Subject Classification. 62D05. Key words and phrases. NFL home-field advantage; hypothesis testing; paired differences test; cold weather teams. ©2021 Proceedings of International Mathematical Sciences. Submitted on 14.06.2021, Accepted on 28.06.2021. Communicated by Ibrahim Canak. 10 COLD WEATHER TEAMS IN THE NATIONAL FOOTBALL LEAGUE ... 11 city of Super Bowl game was the home stadium of a team that participated, which brings the number of home games of the first team to 269 [5]. In completion, this research project is trying to reject the null hypothesis that there is not a significant advantage for the Cold Weather Teams, during the months of December, January, and February.

2. Method and Materials The research project defines home games as games that are played at ateam’s home-field or was voluntarily played at a neutral site in agreement with theNFL that the game would count as a home game for that team in order to include games played in , , and other places. The definition used to deter- mine “cold weather games” was if the game was played in December, January, or February of any given league season. In reference to “cold weather teams” this is for teams that play in an outdoor environment (not a dome) above the 39◦N latitude line. These teams include the Bears (Memorial Stadium used in 2002 at 40.099365234◦N [6], used from 2003-Present at 41.8625332◦N) [7], ( used from 1957-Present at 44.501389◦N)[8], ( used from 1972-Present at 39.048889◦N) [9], (Bills Stadium used from 1973-Present at 42.774◦N [10] and “ Series” from 2008-2011 at the , Toronto Canada [11] at 43.641438◦N)[12], (FirstEnergy Stadium used from 1999-Present at 41.506111◦N)[13], ( used from 2000- Present at 39.095◦N)[14], (Empower Field at Mile High used from 2001-Present at 39.743952◦N)[15], ( used from 2002-Present at 42.091◦N)[16], ( used from 2001-Present at 40.446667◦N)[17], Eagles ( used from 1971-2002 at 39.906667◦N[18], used from 2003-Present at 39.900833◦N)[19], Seahawks ( used from 2002-Present at 47.5952◦N) [20], Ravens (M&T Bank Stadium used from 1998-Present at 39.278056◦N)[21], Jets and Giants ( used from 1984-2009 at 40.812222◦N [22], MetLife Stadium used from 2010-Present at 40.813528◦N)[23], and (TCF Bank Stadium [64] used from 2014-2015 at 44.976◦N)[24]. The research only takes into account home games from the 2002 season and on- wards because that is when the Texans became the 32nd team in the NFL [25].

3. Results Between the years 2002-2020, there were 5057 games in this time period. The overall record of all teams was 5046-5046-22 which gives you an overall winning per- centage of 50% or 0.50. This will allow this study to assume the odds of winning or losing a football game in the NFL is 50/50 probability and is random which is de- fined by “events that cannot be predicted with certainty, but the relative frequency with which they occur in a long series of trials is often remarkably stable,” [26]. The table and graph below shows this phenomenon is associated with NFL teams and their winning percentage, home-field winning percentage, and cold weather winning percentage from 2002-2019 and 2002-2020. *Winning percentage was calculated by taking (wins + (ties*0.5))/(total number of games).* 12 BRANDON JOLY AND MEHMET DIK

Table 1: NFL Teams Winning Percentages Table.

NFL Winning Percentages [27] Team 2002- 2002- Home- Home- Cold Cold 2019 2020 field field Weather Weather 2002- 2002- 2002- 2002- 2019 2020 2019 2020 Fal- 0.528 0.514 0.587 0.570 0.587 0.562 cons (Atl) [28] Arizona Car- 0.448 0.450 0.568 0.564 0.640 0.623 dinals (Ari) [29] Baltimore 0.580 0.585 0.720 0.715 0.673 0.691 Ravens (Bal) [30] Buffalo Bills 0.434 0.456 0.521 0.545 0.489 0.531 (Buf) [31] Carolina 0.522 0.511 0.567 0.551 0.660 0.633 Panthers (Car) [32] Cincinnati 0.463 0.453 0.537 0.529 0.553 0.540 Bengals (Cin) [33] Chicago 0.481 0.481 0.547 0.538 0.500 0.491 Bears (Chi) [34] Cleveland 0.310 0.331 0.378 0.398 0.351 0.364 Browns (Cle) [35] Dallas Cow- 0.540 0.531 0.584 0.580 0.462 0.488 boys (Dal) [36] Denver 0.563 0.550 0.647 0.627 0.66 0.635 Broncos (Den) [37] Li- 0.356 0.353 0.444 0.428 0.333 0.310 ons (Det) [38] Houston 0.453 0.443 0.540 0.525 0.542 0.510 Texans (Hou) [39] Green Bay 0.606 0.615 0.697 0.703 0.745 0.750 Packers (GB) [40] 0.620 0.621 0.697 0.699 0.759 0.768 Colts (Ind) [41] COLD WEATHER TEAMS IN THE NATIONAL FOOTBALL LEAGUE ... 13

Continuation of Table 6 Team 2002- 2002- Home- Home- Cold Cold 2019 2020 field field Weather Weather 2002- 2002- 2002- 2002- 2019 2020 2019 2020 Jacksonville 0.398 0.381 0.483 0.464 0.500 0.479 Jaguars (Jax) [42] Kansas City 0.525 0.544 0.592 0.605 0.630 0.644 Chiefs (KC) [43] Las Vegas 0.360 0.367 0.432 0.422 0.422 0.396 Raiders (LVR) [44] 0.537 0.532 0.591 0.586 0.588 0.593 Chargers (LAC) [45] Los Angeles 0.419 0.430 0.476 0.490 0.422 0.447 Rams (LAR) [46] Miami Dol- 0.438 0.448 0.503 0.510 0.551 0.558 phins (Mia) [47] Minnesota 0.515 0.511 0.649 0.635 0.592 0.588 Vikings (Min) [48] New Eng- 0.761 0.746 0.838 0.829 0.838 0.829 land Patriots (NE) [49] New York 0.488 0.483 0.490 0.484 0.404 0.400 Giants (NYG) [50] New York 0.452 0.435 0.531 0.510 0.581 0.578 Jets (NYJ) [51] Philadelphia 0.580 0.565 0.609 0.601 0.600 0.596 Eagles (Phi) [52] Pittsburgh 0.637 0.640 0.706 0.710 0.724 0.710 Steelers (Pit) [53] San Fran- 0.460 0.456 0.557 0.535 0.630 0.592 cisco 49ers (SF) [54] Seattle Sea- 0.578 0.585 0.703 0.707 0.702 0.689 hawks (Sea) [55] 14 BRANDON JOLY AND MEHMET DIK

Continuation of Table 6 Team 2002- 2002- Home- Home- Cold Cold 2019 2020 field field Weather Weather 2002- 2002- 2002- 2002- 2019 2020 2019 2020 Tampa Bay 0.416 0.438 0.449 0.462 0.333 0.375 Buccaneers (TB) [56] Tennessee 0.485 0.494 0.534 0.535 0.571 0.558 Titans (Ten) [57] 0.401 0.402 0.445 0.439 0.311 0.292 Football Team (WFT) [58] 0.574 0.583 0.612 0.617 0.509 0.517 Saints (NO) [59] End of Table-*all decimals were rounded to the nearest thousandth*

Figure 1. Graph: Scatterplot showing teams winning percentages.

This data was used and then compiled on a season by season basis to construct the following table and graph. COLD WEATHER TEAMS IN THE NATIONAL FOOTBALL LEAGUE ... 15

Table 2: Entire NFL Winning Percentage Season By Season Table.

Entire NFL Winning Percentage Season By Season Year Home Games Cold Weather Team Games at Home During December, January, and February 2002 0.5883458647 0.6829268293 2003 0.6127819549 0.7105263158 2004 0.5676691729 0.625 2005 0.5827067669 0.6363636364 2006 0.5413533835 0.575 2007 0.5714285714 0.6315789474 2008 0.5695488722 0.6129032258 2009 0.5751879699 0.5526315789 2010 0.5526315789 0.5909090909 2011 0.5751879699 0.619047619 2012 0.5733082707 0.5853658537 2013 0.5996240602 0.6097560976 2014 0.5770676692 0.6216216216 2015 0.5413533835 0.5652173913 2016 0.5864661654 0.6888888889 2017 0.5714285714 0.5609756098 2018 0.5977443609 0.6341463415 2019 0.5206766917 0.6341463415 2020 0.5 0.5909090909 End of Table

The overall winning percentages for home games including the 2020 NFL sea- son is 0.5686177576 and without the 2020 season is 0.5724728488. Similarly, the overall winning percentages for Cold Weather Teams including the 2020 season is 0.617076326 and without 0.6186556927. These numbers will vary from the mean due to a different number of games being played every season. For this set ofdata we found the mean (¯x), population standard deviation (σ), and sample standard de- viation (s) for home games, Cold Weather Team games at home during December, January, and February, and all team games at home during December, January, and February for with data that included and was without the 2020 NFL season. Table of Standard Deviations and Arithmetic Means with the 2020 Season Mathematical Home games Cold Weather All Team Games at Method Team Games at Home During De- Home During cember, January, December, January and February x¯ arithmetic mean 0.5686584883 0.6172586568 0.566979456 s sample standard 0.02750025926 0.04325904819 0.05386899073 deviation σ population stan- 0.02676678683 0.04210526565 0.05243222539 dard deviation 16 BRANDON JOLY AND MEHMET DIK

Figure 2. Graph 2: This is the NFL winning percentages for all home teams and cold weather teams including the 2020 season.

Table of Standard Deviations and Arithmetic Means without the 2020 Season Mathematical Home games Cold Weather All Team Games at Method Team Games at Home During De- Home During cember, January, December, January and February x¯ arithmetic mean 0.5724728488 0.6187225216 0.5715965942 s sample standard 0.0225400042 0.04402629073 0.0514169134 deviation σ population stan- 0.0219049467 0.04278586389 0.04996825811 dard deviation 1 Pn The formula used for the arithmetic mean (¯x) wasx ¯= n i=1 xi, where n= number of values and xi= data set values. q PN 2 i=1(xi−x¯) The formula used for sample standard deviation (s) was s= N−1 where N=the number of observations, xi= data set values, and (¯x) is the arithmetic mean. q PN 2 i=1(xi−µ) The formula used for population standard deviation (σ) was σ = N−1 N=the number of observations, xi= data set values, and (µ) is the population mean. In this case, µ =x ¯ because the study has a set number of data points. For the purpose of this study, the study will run 4 hypotheses tests because the 2020 NFL season was considered an outlier. An outlier is “data values that are very different from other measurements in the data set.” [60] The study assumes based on Las Vegas and the gambling markets assumption in making their lines and odds that home-field advantage exists within the NFL and is shown through hometeams having a winning percentage of 0.5686177576 and 0.5724728488 (when you don’t include the 2020 NFL season) [61]. The tests run will be a right-tailed dependent samples paired differences test because the samples can be deemed to be dependent COLD WEATHER TEAMS IN THE NATIONAL FOOTBALL LEAGUE ... 17 on the other since a home game of cold weather teams during December, January, and February will also be included in the sample of all team games at home during December, January, and February and all home games. Thus, this clearly passes the definition of dependent samples being “each data value in one sample canbe paired with a corresponding data value in the other sample,” [60]. Using the test outlines and tables provided by Brasse and Brasse (2009), the tests were done as follows.

3.1. Test 1: Cold Weather Teams Games at Home During December, January, and February, and All Team Games at Home During December, January, and February (including the 2020 NFL Season). . H0 : µd = 0, H1 : µd > 0, α = 0.01 The study begins by pairing the seasons together as a pair. For instance, 2002 Cold Weather Team Winning Percentage with All Team Home Games During De- cember, January, and February Winning Percentage which leaves the following table. Table 3: Paired Differences Table for Test 1.

Paired Differences Table Season Cold Weather All Team Games at D=B-A Team Games at Home during De- Home During De- cember, January, cember, January, and February (A) and February (B) 2002 0.6829268293 0.6136363636 0.06929046563 2003 0.7105263158 0.6623376623 0.04818865345 2004 0.625 0.5888888889 0.03611111111 2005 0.6363636364 0.5444444444 0.09191919192 2006 0.575 0.4494382022 0.1255617978 2007 0.6315789474 0.606741573 0.02483737433 2008 0.6129032258 0.64 -0.02709677419 2009 0.5526315789 0.5444444444 0.008187134503 2010 0.5909090909 0.5222222222 0.06868686869 2011 0.619047619 0.5888888889 0.03015873016 2012 0.5853658537 0.5730337079 0.01233214579 2013 0.6097560976 0.5862068966 0.02354920101 2014 0.6216216216 0.5466666667 0.07495495495 2015 0.5652173913 0.5161290323 0.04908835905 2016 0.6888888889 0.6 0.08888888889 2017 0.5609756098 0.6153846154 -0.05440900563 2018 0.6341463415 0.5730337079 0.0611126336 2019 0.6341463415 0.5172413793 0.1169049622 2020 0.5909090909 0.4838709677 0.1070381232

¯ From the table, the study finds that d = 0.05027920086 and sd = 0.04720562542. n=19. d¯ 0.05027920086 t = s = =4.64241 √d 0.04720562542√ n 19 d.f.=n-1=19-1=18 18 BRANDON JOLY AND MEHMET DIK

The P-value falls to the right of 3.922 from the “Critical Values for Student’s t distribution.” 3.922 < P-Value for the sample t. Since the interval containing the P-Value of sample t lies to the right of α = 0.01, we reject H0. At the 1% level of significance and even the 0.1% level of significance, we conclude that the Cold Weather Team Games at Home During December, January have an advantage over All Team Games at Home During December, January, and February which includes the 2020 season.

3.2. Test 2: Cold Weather Teams Games at Home During December, January, and February, and All Team Games at Home During December, January, and February (without the 2020 NFL Season). . H0 : µd = 0, H1 : µd > 0, α = 0.01 The study begins by pairing the seasons together as a pair. For instance, 2002 Cold Weather Team Winning Percentage with All Team Home Games During De- cember, January, and February Winning Percentage which leaves the following table. Table 4: Paired Differences Table for Test 2.

Paired Differences Table Season Cold Weather All Team Games at D=B-A Team Games at Home during De- Home During De- cember, January, cember, January, and February (A) and February (B) 2002 0.6829268293 0.6136363636 0.06929046563 2003 0.7105263158 0.6623376623 0.04818865345 2004 0.625 0.5888888889 0.03611111111 2005 0.6363636364 0.5444444444 0.09191919192 2006 0.575 0.4494382022 0.1255617978 2007 0.6315789474 0.606741573 0.02483737433 2008 0.6129032258 0.64 -0.02709677419 2009 0.5526315789 0.5444444444 0.008187134503 2010 0.5909090909 0.5222222222 0.06868686869 2011 0.619047619 0.5888888889 0.03015873016 2012 0.5853658537 0.5730337079 0.01233214579 2013 0.6097560976 0.5862068966 0.02354920101 2014 0.6216216216 0.5466666667 0.07495495495 2015 0.5652173913 0.5161290323 0.04908835905 2016 0.6888888889 0.6 0.08888888889 2017 0.5609756098 0.6153846154 -0.05440900563 2018 0.6341463415 0.5730337079 0.0611126336 2019 0.6341463415 0.5172413793 0.1169049622

¯ From the table, the study finds that d = 0.0471259274 and sd = 0.04646955209. n=18. d¯ 0.0471259274 t = s = =4.30345 √d 0.04646955209√ n 18 d.f.=n-1=18-1=17 COLD WEATHER TEAMS IN THE NATIONAL FOOTBALL LEAGUE ... 19

The P-value falls to the right of 3.965 from the “Critical Values for Student’s t distribution.” 3.965< P-Value for the sample t. Since the interval containing the P-Value of sample t lies to the right of α = 0.01, we reject H0. At the 1% level of significance and even the 0.1% level of significance, we conclude that the Cold Weather Team Games at Home During December, January have an advantage over All Team Games at Home During December, January, and February which does not include the 2020 season.

3.3. Test 3:Cold Weather Teams Games at Home During December, Jan- uary, and February, and All Home Games (including the 2020 NFL Sea- son). . H0 : µd = 0, H1 : µd > 0, α = 0.01 The study begins by pairing the seasons together as a pair. For instance, 2002 Cold Weather Team Winning Percentage with All Team Home Games Winning Percentage which leaves the following table.

Table 5: Paired Differences Table for Test 3.

Paired Differences Table Season Cold Weather All Team Games at D=B-A Team Games at Home (A) Home During De- cember, January, and February (B) 2002 0.6829268293 0.5883458647 0.09458096461 2003 0.7105263158 0.6127819549 0.0977443609 2004 0.625 0.5676691729 0.05733082707 2005 0.6363636364 0.5827067669 0.05365686945 2006 0.575 0.5413533835 0.03364661654 2007 0.6315789474 0.5714285714 0.06015037594 2008 0.6129032258 0.5695488722 0.04335435363 2009 0.5526315789 0.5751879699 -0.02255639098 2010 0.5909090909 0.5526315789 0.03827751196 2011 0.619047619 0.5751879699 0.04385964912 2012 0.5853658537 0.5733082707 0.01205758298 2013 0.6097560976 0.5996240602 0.01013203741 2014 0.6216216216 0.5770676692 0.04455395245 2015 0.5652173913 0.5413533835 0.02386400785 2016 0.6888888889 0.5864661654 0.1024227235 2017 0.5609756098 0.5714285714 -0.01045296167 2018 0.6341463415 0.5977443609 0.03640198056 2019 0.6341463415 0.5206766917 0.1134696497 2020 0.5909090909 0.5 0.09090909091

¯ From the table, the study finds that d = 0.04860016852 and sd = 0.03813895447. n=19. d¯ 0.04860016852 t = s = =5.55579 √d 0.03813895447√ n 19 d.f.=n-1=19-1=18 20 BRANDON JOLY AND MEHMET DIK

The P-value falls to the right of 3.922 from the “Critical Values for Student’s t distribution.” 3.922 < P-Value for the sample t. Since the interval containing the P-Value of sample t lies to the right of α = 0.01, we reject H0. At the 1% level of significance and even the 0.1% level of significance, we conclude that the Cold Weather Team Games at Home During December, January have an advantage over All Home Games which includes the 2020 season. 3.4. Test 4:Cold Weather Teams Games at Home During December, Jan- uary, and February, and All Home Games (without the 2020 NFL Sea- son). . H0 : µd = 0, H1 : µd > 0, α = 0.01 The study begins by pairing the seasons together as a pair. For instance, 2002 Cold Weather Team Winning Percentage with All Team Home Games Winning Percentage which leaves the following table.

Table 6: Paired Differences Table for Test 4.

Paired Differences Table Season Cold Weather All Team Games at D=B-A Team Games at Home (A) Home During De- cember, January, and February (B) 2002 0.6829268293 0.5883458647 0.09458096461 2003 0.7105263158 0.6127819549 0.0977443609 2004 0.625 0.5676691729 0.05733082707 2005 0.6363636364 0.5827067669 0.05365686945 2006 0.575 0.5413533835 0.03364661654 2007 0.6315789474 0.5714285714 0.06015037594 2008 0.6129032258 0.5695488722 0.04335435363 2009 0.5526315789 0.5751879699 -0.02255639098 2010 0.5909090909 0.5526315789 0.03827751196 2011 0.619047619 0.5751879699 0.04385964912 2012 0.5853658537 0.5733082707 0.01205758298 2013 0.6097560976 0.5996240602 0.01013203741 2014 0.6216216216 0.5770676692 0.04455395245 2015 0.5652173913 0.5413533835 0.02386400785 2016 0.6888888889 0.5864661654 0.1024227235 2017 0.5609756098 0.5714285714 -0.01045296167 2018 0.6341463415 0.5977443609 0.03640198056 2019 0.6341463415 0.5206766917 0.1134696497

¯ From the table, the study finds that d = 0.04624967283 and sd = 0.03780207387. n=18. d¯ 0.04624967283 t = s = =5.18993 √d 0.03780207387√ n 18 d.f.=n-1=18-1=17 The P-value falls to the right of 3.965 from the “Critical Values for Student’s t distribution.” 3.965 < P-Value for the sample t. COLD WEATHER TEAMS IN THE NATIONAL FOOTBALL LEAGUE ... 21

Since the interval containing the P-Value of sample t lies to the right of α = 0.01, we reject H0. At the 1% level of significance and even the 0.1% level of significance, we conclude that the Cold Weather Team Games at Home During December, January have an advantage over All Home Games which does not include the 2020 season.

4. Discussion These results mean that although prior studies conclusions have shown that the impact of home-field advantage decreases year over year, it has been shown that NFL teams playing in an outdoor environment (not a dome) above the 39◦N latitude line have a statistically significant advantage over teams whose home is below the the 39◦N latitude line or play in a controlled playing environment (a dome) [62,63]. The results suggest that Cold Weather Teams have been more successful on average at home than non cold weather teams. This would imply these teams win more division titles, Round games, Divisional Round games, Conference Championships, and participate in more Super Bowls. As for this data, of the 19 years studied, 15 of 19 of the years included Cold Weather Teams winning the Super Bowl or World Championship Game of the NFL (New England Patriots with 5 Super Bowls in 2003, 2004, 2014, 2016, and 2018 seasons, with 2 Super Bowls in 2007 and 2011 seasons, Pittsburgh Steelers with 2 Super Bowls in 2005 and 2008, and 6 teams with 1 Super Bowl title), 10 of 19 Super Bowl Runner Ups, 28 of 38 American Football Conference (AFC) Championship Game teams, and 17 of 38 National Football Conference (NFC) Championship Game Teams. These results matter because this could change how betting services such as DraftKings and FanDuel set the lines for games in December, January, and February. These results could also be used so that the average fan could understand how much weather and more specifically colder weather and snow plays a factor in the outcome of a game. The data gathered is very reliable as it is winning percentages that are based off of NFL data. The potential mistake comes asthere are a different amount of cold weather games every year which could cause varying differences in the means. Other reasons for limitations on results are thatColder Weather Teams have been very successful which could have skewed the results as playoff games are held at the stadium of the higher seeded team and theseteams were successful during December, January, and February to reach these points. The limitation to only 19 years also affects the results and this data could be expanded to the entire Super Bowl era of the NFL beginning in 1967 for a larger sample size of results. More research could go into what types of weather have a larger impact on games or try to determine the full causes of weather on playing capacity of NFL players.

5. Conclusion By the results of this article, the research project rejected the null hypothesis and left no doubt that Cold Weather Teams have a mathematically significant advantage over all other NFL teams during December, January, and February and in comparison to all other times of the year. However, the NFL is constantly changing to bigger and better stadiums with teams shifting to more indoor environments for playing games. For that reason, these results may be ever changing and with players such as who has played through the duration of this study with mainly 22 BRANDON JOLY AND MEHMET DIK the New England Patriots and contributed to 5 Super Bowls during this period, the ebb and flow of the NFL success was not able to be adequately seen. Yet,the NFL’s Cold Weather Teams thrived in late season games and provided for lots of success which resulted in the conclusion of a statistical advantage for them. 2020 was the perfect year for weather to play the biggest factor as many teams had the second biggest d value because fans and their impact was in a sense controlled. Since 2020 had a big d value and all of the paired differences tests rejected the null hypothesis, this research project ultimately concluded that Cold Weather Teams during December, January, and February have a statistically significant advantage over other teams.

Acknowledgements. I would like the thank the 5th International Conference of Mathematical Sciences (ICMS 2021) for the opportunity to publish and present these findings. I would like to thank Mehmet Dik for providing me this opportunity to do this research. The late Ranjan Roy for pushing me to pursue mathematics further and the Green Bay Packers and Packers Pro Shop for allowing me to do this research.

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Brandon Joly, 700 College Street Beloit College Box 693, Beloit, Wisconsin, USA 53511, Phone: (920)639-3849 Email address: [email protected]

Mehmet Dik, 700 College Street, Beloit, Wisconsin, USA 53511, Phone: (815)226-4135 Email address: [email protected]